Can we please keep in mind that he adamantly tried to persuade Uther to let him go and save Merlin and after he successfully retrieved the flower said he didn't care how much Uther punished him as long as Merlin received the remedy.
Furthermore shall we recall how Arthur did not 'sit there and do nothing' while Merlin's village was attacked but, against the orders of his father, went alone to help Merlin and trained the men there despite their slim chances of winning, in turn placing his life on the line for Merlin.
Or how about the time Merlin was captured by Morgana in A Servant of Two Masters and Arthur would not rest until Merlin was found whilst others quickly lost hope. In that episode he even went on to say Merlin was the only person he could trust. Need I go on?
My point is there are numerous moments that are testaments to their strong friendship and if you cannot see that I genuinely feel sorry for you. I hope you reconsider your view towards this.